Math specialists will be available to tutor tomorrow, Friday (and Fridays from now on) – more days will be announced soon.
Fridays beginning tomorrow from
10 am to 6 pm in MAT 065 through MAT 2675.
Tutoring will take place in room N723.
Category: Uncategorized
Questions to use with the Lines Lab WeBWorK assignment
Questions for the Lines Lab:
Give a definition of x-intercept and y-intercept.
What is the y-coordinate of the x-intercept?
What is the x-coordinate of the y-intercept?
How can you use the two intercepts to find the equation of the line?
Does a line always have an x-intercept? (If not, give an example.)
Does a line always have a y-intercept? Why or why not? (If not, give an example.)
Are there any lines that have neither an x-intercept nor a y-intercept?
Notes for Thursday 5 September class
Here is the link for information about accessing your City Tech email account.
Notes from last time: **Still being updated!**
I solved a linear system by graphing, and another system by the method of substitution and then by the method of elimination (in two ways). You must know these methods very thoroughly and be able to use them both.
• Active learning practice solving a system of 2 linear equations in 2 variables by substitution and elimination
• Solving a system of 3 linear equations in 3 variables (active learning with outline notes)
The two outline notes pages which I handed out in class are also available here:
There is a very nice video explaining this method at Patrick’s Just Math Tutorials. He explains the reasoning along the way.
There is a longer video explanation of the method along with background information about 3 by 3 systems at Khan Academy.
Make sure to answer (in your notebook) the Questions that go with the Lines Lab assignment.
Notes from first two class meetings
These are still being edited!!!
Here is a supplement to the textbook which covers everything about lines that we need to know:
Important information about lines and linear equations: (And equations in general)
A solution to an equation in two variables is an ordered pair (a point in the coordinate plane) which satisfies that equation.
The graph of any equation is a picture of the set of all solutions to that equation.
A linear equation is an equation in which all variables are to the first power (and no term contains more than one variable).
The graph of a linear equation in two variables is a line.
Note: “line” in mathematics always means a straight line.
The slope of a line in the plane measures how “tilted” that line is. Another way to say this: the slope gives the direction of the line. It represents the rate of change of the y-values.
Definition: given any two points on a line, $A = (x_A, y_A)$ and $B = (x_B, y_B)$, the slope of the line is defined as $m = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x} = \frac{y_A – y_B}{x_A – x_B}$
Three important forms of the equation of a line:
Slope-intercept form – the most important, usually
$y = mx + b$
where $m$ is the slope of the line and $b$ is the y-intercept.
Either $m$ or $b$ or both may be 0.
“Standard” form
Ax + By + C = 0
Point-slope form: if $(x_A, y_A)$ is a point on the line
$y – y_A = m(x – x_A)$
Parallel lines have the same slopes.
Perpendicular lines are lies which intersect in a right angle. Their slopes are negative reciprocals: if one of the slopes is $\frac{a}{b}$, the other slope is $-\frac{b}{a}$.
Another way to say this: the product of the two slopes is-1.
